Modeling and analysis of a cooperative service network

Highlights

• We develop a detailed stochastic model to analyze a cooperative service network design.

• Our analysis captures dynamics of customer arrivals, assignment, and admission control.

• We derive analytical results on dynamic admission problem of a non-preemptive server.

• We determine optimal number of participants in the network to maximize the profit.

• We determine optimal service price for the network customers.

Abstract

With the advances in technology and changes in customers’ attitude towards different service delivery formats, it is important for the service providers to deliver online services in addition to the traditional face-to-face services. In the cooperative service network presented in this study, service providers cooperate to serve online service requests received by the network in addition to their own customers. Designing and managing the cooperative network effectively increase the utilization of the involved servers, provide an adequate service for the external customers, and increase the profit for both the network and service providers. From the operational perspective, the number and utilization of the members to be included in the network and the price that will be paid to each member for a directed request are the main design questions. In order to answer these questions, we present a stochastic model that captures the dynamics of customer arrivals, assignment, and admission control. To establish this model, we first derive the solution of the dynamic admission control problem for the servers who decide how to admit their own customers and the external online customers using a Markov decision process. We then analyze the operation of the whole network with the servers who use the optimal admission control policy and obtain the system performance measures depending on the members’ operational parameters. These results are used to determine the optimal number of servers in the network and the service price to be paid to the participating servers in order to maximize the obtained profit. We show that a cooperative service network is an effective way of utilizing the idle capacity of the servers while providing an adequate service level for the external online customers and increasing the profit for both the network and service providers.

Introduction

Technology has improved the ways of delivering services to the customers (Snyder et al., 2016). As one of the significant advances, online services lead to a more convenient access for the customers and a utilization improvement for the providers (Zhang and Prybutok, 2005, Ostrom et al., 2015). Online services enable the service providers to serve not only the customers who come to the service centers but also the external customers over a distance. Although some customers still prefer to have a direct in person interaction with the service providers, online services help to target the customers who want to be served without any cost of traveling (Fernández-Sabiote and Román, 2012). Hence, there is a significant potential to offer online services in addition to traditional face-to-face services by the service providers (Berry et al., 2002, Ostrom et al., 2015).

Based on this motivation, we focus on a cooperative service network which is formed by a group of independent cooperating service providers. Each server serves the stream of his own customers independently of the network structure at the service facility. The cooperative network enables the servers to access online external customers who request for the remote service by using the network online platform. A telemedicine platform is a good example of cooperative service networks. It is a group of cooperating healthcare providers who deliver healthcare services over a distance through an easy to use on-line network using the means of information technology (Roine et al., 2001, Norris, 2002, Craig and Petterson, 2005, Whitten et al., 2010). It is crucial to design these platforms in a way to provide profitable and efficient service for the customers (Körpeoğlu et al., 2014). Based on the operational parameters of the service providers, designers should decide on the characteristics of the servers to be included in the cooperative network as well as the optimal number of participants. These decisions are dependent on the servers’ admission policy to serve their own customers and external customers. Moreover, the network needs to decide about the service price to pay the members for serving external customers. This price should be high enough to convince the servers to participate in the network while it should result in a profitable network operation with respect to the market price set externally for online services. In order to answer these questions about designing and managing a cooperative service network, we develop a stochastic model that captures the operation of the network with the dynamics of customer arrivals, assignment, and admission control. We use this model to determine the optimal number of servers and the service price to be offered to the service providers in order to maximize the expected profit while achieving an adequate service level for the external customers. We then make general observations about the effects of the servers’ utilization rate, the external customers’ arrival rate, and the service price on the optimal decisions. We show that in an optimally designed cooperative network, the members benefit from pooling their excess capacity to serve external customers and hence increasing their utilization and obtained profit.

There are a large number of studies focused on the cooperation-based business models for service networks by pooling the individual streams of customers. Our paper differs from the other ones in the literature since we consider a type of cooperative operation that allows the members to receive and serve their own customers independent of the cooperation structure. This assumption is consistent with the industrial practice for the service providers who wish to add another channel to offer a service in addition to their previous mode of serving customers. The service providers in the proposed network decide about their availability for the external customers. In response to the servers’ admission policy, the network defines the optimal number of members and the service price for the external customers. Different from the other works that focus on the profit of the whole service network, we discuss profit of each member at the first step. Accordingly, we establish a relatively simple sufficient condition for the service price to identify whether participation in the network is economically feasible for the servers. We then turn into the whole network’s profit to define the optimal design.

The main contribution of this work is twofold. First, we provide a detailed operational model of a cooperative network among a number of independent servers with embedded optimal dynamic admission decisions. This operational model is then used for determining the optimal design of the network. To the best of our knowledge, this is the first study that addresses the optimal design of a cooperative network based on the analytical analysis of the structure with the optimal operational decisions. Second, we extend the literature on the analysis of queueing systems with non-preemptive service order and heterogeneous customer streams. We prove that the optimal dynamic admission policy is a non-preemptive threshold-type policy in these kind of systems.

The organization of the remaining parts of this paper is as follows: In Section 2, we review the related literature. We present the model, its assumptions and also explain the two main stages of our analysis in Section 3. In Section 4, we give the dynamic programming formulation for each server’s operation and derive the optimal admission policy for the customers. Then, we perform the stationary analysis of this operation using a queueing model and obtain the stationary optimal admission policy for the service providers. Based on our results from Section 4, we analyze the operation of the network in Section 5 and determine the optimal number of servers to achieve the desired performance of the network. Our numerical results and discussion regarding the efficient design of the network are given in Section 6. Finally, Section 7 is devoted to concluding remarks.